MediumCalculusca-123

Beta Function Derivative

Problem

The derivative of the beta function with respect to its first argument is dB/da = B(a, b) * (psi(a) - psi(a + b)), where psi is the digamma function.

Given positive integers a and b, compute B(a, b) = Gamma(a)*Gamma(b)/Gamma(a+b) with math.gamma and evaluate digamma with psi(n) = -gamma + H_{n-1}. Return the derivative.

Hint

Differentiating under the integral sign brings down a factor log(t).

Test cases

case 1

in: [1,1]

expected: -1

case 2

in: [2,3]

expected: -0.09027777777777779

case 3

in: [3,3]

expected: -0.02611111111111111

case 4

in: [1,5]

expected: -0.45666666666666667

Starter codePython

def beta_derivative(a, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor